**数学与系统科学研究院**

**计算数学所学术报告**

**报告人**：
M. Zuhair Nashed

University of Central Florida, USA

**报告题目**
Inverse Problems and Recovery Problems from Partial Information: The Magic of Signal Analysis

**Abstract:**
Inverse Problems deal with determining for a given input-output system an input that produces an observed output, or of determining an input that produces a desired output. In terms of an operator T acting between say two normed spaces X and Y, the problem of solving the equation T(x) = y for given data y Y is a canonical example of an inverse problem. Typically inverse problems are ill-posed. Important examples of ill-posed inverse problems include integral equations of the first kind, tomography, and inverse scattering. Signal Analysis/Processing deals with digital representations of signals and their analog reconstructions from digital representations. Image Analysis deals with problems such as image recovery, enhancement, feature extraction, and motion detection. Medical Imaging is an important branch of Image Science and deals with image analysis in medical applications.

The common thread among the areas of Inverse Problems, Signal Analysis and Image Analysis is a canonical problem: recovery of an object (function, signal, picture) from partial or indirect information about the object (often contaminated by noise). Both Inverse Problems and Imaging Science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of Science, Engineering, Technology, and Medicine. Research in Inverse Problems and Image Processing has rich interactions with several areas of Mathematics, and strong links to Signal Processing, Variational Problems, Applied Harmonic Analysis and Computational Mathematics.

This talk will address the question “What are inverse problems, and what should every scientist know about them?” The philosophy and some of the methodologies of resolution of ill-posedness will be delineated. Finally, interaction of inverse problems and signal analysis/processing will be explored within the framework of sampling expansions and computational harmonic analysis. Examples and ideas will be emphasized, rather than theorems, proofs, or technical details.

**报告时间**：2004年12月27日 下午1：30-2：30

**报告地点**：科技综合楼三层报告厅